Lottery Annuity Calculator

A lottery annuity pays a jackpot $J$ as $N$ installments that each rise by a fixed rate $g$ over the one before. The installments form a geometric series, so the first payment is

$P_1 = \frac{J \cdot g}{(1+g)^N - 1}, \qquad P_k = P_1 (1+g)^{k-1}$

• $J$ — the advertised total, i.e. the sum of all $N$ payments
• $g$ — the annual escalation as a decimal (5% is $0.05$)
• $N$ — the number of installments
• $P_k$ — the $k$-th payment

Use this whenever payments grow at a constant percentage. If they are level instead, set $P = J/N$ — but almost no large game works that way, which is why the first installment is far below $J/N$ and the last one far above it. Escalation rates and payment counts are set by each game's published rules, so take $g$ and $N$ from the official rules and let the formula do the rest.

A stream of $n$ level payments $C$ at periodic rate $r$ has two standard values.

Future value (ordinary annuity, payments at period end):

$FV = C \cdot \frac{(1+r)^n - 1}{r}$

Present value:

$PV = C \cdot \frac{1 - (1+r)^{-n}}{r}$

The fractions are the annuity factors printed in future-value and present-value annuity tables: look up the row for $n$ and the column for $r$, then multiply by $C$. For a single sum rather than a stream, the present value factor is

$\text{PVF} = \frac{1}{(1+r)^n} = (1+r)^{-n}$

If payments arrive at the start of each period — an annuity due — every payment is discounted one period less, so multiply either factor by $(1+r)$.

Comparing a cash lump sum against an annuity only means anything once both are expressed at the same date, which is exactly what $PV$ does. The discount rate you choose drives the answer, so state it explicitly.

• Dividing the jackpot by $N$: with $g > 0$ the payments escalate, so $J/N$ is neither the first nor a typical payment.
• Confusing escalation with discounting: $g$ grows the payments, $r$ discounts them. They are different rates and both can appear in one problem.
• Mismatching $r$ and $n$: monthly payments need a monthly rate and a count of months.
• Using an ordinary-annuity factor for an annuity due: that understates the value by a factor of $(1+r)$.
• Reading a jackpot's cash option as "the annuity minus tax": it is a present value, computed before any withholding.
• Treating the result as a tax or payout figure: this page does arithmetic on the numbers you enter. Actual game rules, withholding and final tax liability depend on the game and your jurisdiction.